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Tue Oct 4 17:16:20 2016 UTC (2 years, 5 months ago) by glk
File size: 7485 byte(s)
Tue Oct 4 17:16:20 2016 UTC (2 years, 5 months ago) by glk
File size: 7485 byte(s)
stray whitespace; clarifying stabilization message
/* ========================================== Mutually-repelling particles populating a unit sphere This is heavily based on the [`circle.diderot`](../circle) example; see that program for more detailed and explanatory comments. The new things added with this example are documented in comments below. A significant capability demonstrated here is "population control", whereby particles create new particles (using `new`) if there seem to be too few, or die if there are too may (using `die`). Along with this there is a new variable `undone` that acts as a signal (to the global update method monitoring the computation) that things are unfinished because the system population is changing. ... TODO: example of running program and looking at output ========================================== */ input vec3{} ipos ("initial positions for all particles") = load("vec3.nrrd"); input real rad ("radius of particle's potential energy support") = 0.1; input real eps ("system convergence threshold, computed as the coefficient-of-variation of distances to nearest neighbors") = 0.05; input int pcp ("periodicity of population control (if greater than zero)") = 2; input real hhInit ("initial step size for potential energy gradient descent") = 1; real newDist = 0.5*rad; // how far away to birth new particles real stepMax = rad; // limit on distance to travel per iter int iter = 0; // which iteration we're on // Univariate energy functions; see ../circle/circle.diderot for alternatives function real phi(real r) = (1 - r)^4; function real phi'(real r) = -4*(1 - r)^3; // Energy and force from particle (with radius rad) at vec3 x function real enr(vec3 x) = phi(|x|/rad); function vec3 frc(vec3 x) = phi'(|x|/rad) * (1/rad) * x/|x|; // chain rule // Returns a non-zero vector perpendicular to given non-zero vector v function vec3 perp3(vec3 v) { int c = 0; if (|v[0]| < |v[1]|) { c = 1; } // not v[c] because tensors can only be indexed by constants if (|v[1] if 1==c else v[0]| < |v[2]|) { c = 2; } // now c is index of v component with largest absolute value vec3 ret = ([v[1] - v[2], -v[0], v[0]] if (c == 0) else [-v[1], v[0] - v[2], v[1]] if (c == 1) else [-v[2], v[2], v[0] - v[1]]); return ret; } // From a given vec3, find a random-ish value uniformly sampling [0,1) function real posrnd(vec3 v) { vec3 p = 10000*v/rad; return fmod(|fmod(p[0],1)| + |fmod(p[1],1)| + |fmod(p[2],1)|, 1); } // Is this an iteration in which to do population control? function bool pcIter() = (pcp > 0 && iter > 0 && 0 == iter % pcp); /* The particle is initialized at position pos0, with initial stepsize hh0. The first set of particles gets hhInit for the initial stepsize, but new particles created by population control benefit from getting the stepsize that was adaptively learned by the parent. */ strand particle (vec3 pos0, real hh0) { output vec3 pos = pos0/|pos0|; real hh = hh0; vec3 step = [0,0,0]; // step along force real closest = rad; // distance to closest neighbor int ncount = 0; // how many neighbors did we have /* This "undone" variable signals to global update that something is happening or just changed that should delay convergence. In this program it is reset to 1 when new particles are created and when there are too many neighbors; otherwise it is slowly decreased towards 0. */ real undone = 1; update { // compute energy and forces on us from neighbors real energyLast = 0; vec3 force = [0,0,0]; ncount = 0; foreach (particle P in sphere(rad)) { vec3 x = P.pos - pos; if (|x| == 0) { /* we're exactly overlapping with another particle; would be nice to have exactly one strand persist and kill the others; but simpler to have all overlap-ees die here and let population control fill in the hole as needed later */ die; } energyLast += enr(x); force += frc(x); ncount += 1; } vec3 norm = normalize(pos); // surface normal for unit circle if (0 == ncount) { if (pcIter()) { // no neighbors, so let's make one vec3 npos = pos + newDist*normalize(perp3(norm)); new particle(npos, hh); undone = 1; } else { undone *= pow(0.5, 1.0/(2*(pcp if pcp > 0 else 1))); } // set closest to something in case used in global update closest = newDist; continue; } /* Else we have interacting neighbors; project force onto tangent surface, find step, limit step size */ force = (identity[3] - norm⊗norm)•force; step = hh*force; if (|step| > stepMax) { hh *= stepMax/|step|; step = hh*force; } // Take step, re-apply constraint, find new energy vec3 posLast = pos; pos = normalize(pos + step); real energy = 0; closest = rad; ncount = 0; foreach (particle P in sphere(rad)) { energy += enr(P.pos - pos); closest = min(closest, |P.pos - pos|); ncount += 1; } // Armijo-Goldstein sufficient decrease condition if (energy - energyLast > 0.5*(pos - posLast)•(-force)) { hh *= 0.5; // energy didn't decrease as expected: backtrack pos = posLast; // try again next iteration // no progress, so decrease of undone } else { hh *= 1.02; // opportunistically increase step size // indicate progress; may be over-written below undone *= pow(0.5, 1.0/(2*(pcp if pcp > 0 else 1))); // try to have between 5 and 8 neighbors if (pcIter()) { if (ncount < 5) { new particle(pos + newDist*normalize(force), hh); undone = 1; } else if (ncount > 8) { /* If this particle has ncount neighbors, then all of those neighbors probably have a similar number of neighbors. To get down to having about 8 neighbors, all of them should die with a chance of ncount-8 out of ncount. */ if (posrnd(pos) < (ncount - 8.0)/ncount) { die; } // else not done if too many neighbors, w/ population control undone = 1; } } } // Record actual step taken, in case used in global update step = pos - posLast; } } global { /* Compute coefficient-of-variation of distance to closest neighbor */ real meancl = mean { P.closest | P in particle.all}; real varicl = mean { (P.closest - meancl)^2 | P in particle.all}; real covcl = sqrt(varicl) / meancl; real meanncount = mean { real(P.ncount) | P in particle.all}; real maxundone = max { P.undone | P in particle.all}; print("(iter ", iter, ") COV(cl)=", covcl, "; mean(ncount)=", meanncount, "; max(undone)=", maxundone, "\n"); if (covcl < eps // seem to be geometrically uniform && maxundone < 0.5) { // and no particle recently set undone=1 print("Stabilizing ", numActive(), " points with COV(closest) ", covcl, " < ", eps, " and maxundone ", maxundone, " < 0.5 (iter ", iter, ")\n"); stabilize; } iter += 1; } initially { particle(ipos[ii], hhInit) | ii in 0 .. length(ipos)-1 };
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